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Question
Find the geometric means of the following pairs of number:
a3b and ab3
Solution
\[\text { Let the G . M . between }a^3 \text { b and a } b^3 \text { be G } . \]
\[\text { Then,} a^3 \text { b, G and } a b^3 \text { are in G . P } . \]
\[ \therefore G^2 = a^3 b \times a b^3 \]
\[ \Rightarrow G^2 = a^4 b^4 \]
\[ \Rightarrow G = \sqrt{a^4 b^4}\]
\[ \Rightarrow G = a^2 b^2\]
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